anonymous
  • anonymous
Identify the indeterminate form and evaluate the limit using l'Hopital's Rule. The limit as x approaches infinity of ln(x+1)/logbase2 of x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Psymon
  • Psymon
Well, if x is approaching infinity, then straight away we have theindeterminant form infinity over infinity. Since we have the function in an undeterminant form, this satisfies the condition in which we can use l'hopitals rule. Do you know the derivatives of natural log and of logs with bases other than e?
anonymous
  • anonymous
Yeah I know the derivative of logs
Psymon
  • Psymon
Alright, so just take the derivative of the numerator and then divide it by the derivative of the denominator and let's see what we get.

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anonymous
  • anonymous
so for the bottom the derivative would be 1 / xln2 ?
Psymon
  • Psymon
Correct.
anonymous
  • anonymous
do i do the reciprocal of the bottom derivative in order to multiply it by the top derivative ?
Psymon
  • Psymon
Right, so the derivative for the bottom would basically flip and multiply.
anonymous
  • anonymous
so after i get \[\lim_{x \rightarrow \infty}\frac{ x \ln 2 }{ x+1 }\] what do I do ?
Psymon
  • Psymon
Well, we still have an indeterminant form. This means we can just use l'hopitals again.
anonymous
  • anonymous
I use product rule for the top right ?
Psymon
  • Psymon
No need. ln2 is just a constant. So you take the derivative of it in the same way you would like 2x.
anonymous
  • anonymous
so the limit would just be ln2 ?
Psymon
  • Psymon
Yep, thats all it would be :3
anonymous
  • anonymous
Thank you :)
Psymon
  • Psymon
Sure ^_^

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